Unit 2, Lesson 9: Constant Speed

Transcription

1 Unit 2, Lesson 9: Constant Speed Lesson Goals Use a double number line to find the speed expressed in distance traveled per 1 unit of time. Use per language in the context of constant speed. Understand what at the same rate means in the context of moving objects. Experience a context involving constant speed. Required Materials stopwatches string meter sticks masking tape 9.1: Number Talk: Dividing by Powers of 10 (10 minutes) Setup: Display one problem at a time. 1 minute of quiet think time, followed by a whole-class discussion. Student task statement Find the quotient mentally. Possible responses Unit 2: Introducing Ratios, Lesson 9: Constant Speed 1

2 9.2: Moving 10 Meters (25 minutes) Setup: Set up paths as described in lesson plan. Students in groups of 2. Provide a stopwatch. Demonstrate the experiment set-up and data collection process. Unit 2: Introducing Ratios, Lesson 9: Constant Speed 2

3 Student task statement Your teacher will set up a straight path with a 1-meter warm-up zone and a 10-meter measuring zone. Follow the following instructions to collect the data. Possible responses Answers vary. Anticipated misconceptions 1. a. The person with the stopwatch (the timer ) stands at the finish line. The person being timed (the mover ) stands at the warm-up line. b. On the first round, the mover starts moving at a slow, steady speed along the path. When the mover reaches the start line, they say, Start! and the timer starts the stopwatch. Students may have difficulty estimating the distance traveled in 1 second. Encourage them to mark the double number line to help. For example, marking 5 meters halfway between 0 and 10 and determining the elapsed time as half the recorded total may cue them to use division. c. The mover keeps moving steadily along the path. When they reach the finish line, the timer stops the stopwatch and records the time, rounded to the nearest second, in the table. d. On the second round, the mover follows the same instructions, but this time, moving at a quick, steady speed. The timer records the time the same way. e. Repeat these steps until each person in the group has gone twice: once at a slow, steady speed, and once at a quick, steady speed. your slow moving time (seconds) your fast moving time (seconds) Unit 2: Introducing Ratios, Lesson 9: Constant Speed 3

4 2. After you finish collecting the data, use the double number line diagrams to answer the questions. Use the times your partner collected while you were moving. Moving slowly: Moving quickly: a. Estimate the distance in meters you traveled in 1 second when moving slowly. b. Estimate the distance in meters you traveled in 1 second when moving quickly. c. Trade diagrams with someone who is not your partner. How is the diagram representing someone moving slowly different from the diagram representing someone moving quickly? Unit 2: Introducing Ratios, Lesson 9: Constant Speed 4

5 9.3: Moving for 10 Seconds (10 minutes) Setup: Keep students with the same partners. Quiet think time, followed by a partner discussion. Unit 2: Introducing Ratios, Lesson 9: Constant Speed 5

6 Student task statement Lin and Diego both ran for 10 seconds, each at their own constant speed. Lin ran 40 meters and Diego ran 55 meters. 1. Who was moving faster? Explain your reasoning. 2. How far did each person move in 1 second? If you get stuck, consider drawing double number line diagrams to represent the situations. Possible responses 1. Diego ran faster, covering a greater distance in the same amount of time. 2. Lin ran 4 meters per second, and Diego ran 5.5 meters per second. 3. Use your data from the previous activity to find how far you could travel in 10 seconds at your quicker speed. 4. Han ran 100 meters in 20 seconds at a constant speed. Is this speed faster, slower, or the same as Lin s? Diego s? Yours? 3. Answers vary, but 10 times the distance traveled in 1 second. 4. Han ran 5 meters per second, faster than Lin but slower than Diego. Anticipated misconceptions Instead of dividing 40 by 10, some students may instead calculate. Ask them to articulate what the resulting number means (0.25 seconds to travel 1 meter) and contrast that meaning with what the problem is asking (how many meters in one second). Another approach would be to encourage them to draw a double Unit 2: Introducing Ratios, Lesson 9: Constant Speed 6

7 number line and think about how they can figure out what value for distance corresponds to 1 second on the line for elapsed time. Are you ready for more? Lin and Diego want to run a race in which they will both finish when the timer reads exactly 30 seconds. Who should get a head start, and how long should the head start be? Possible Responses Lin needs a 45-meter head start. Lin will travel 120 meters in 30 seconds, and Diego will travel 165 meters in 30 seconds. Lesson Synthesis (5 minutes) How can you decide which of two people is running faster? How do you calculate speed? Why is it useful to know a speed? 9.4: Train Speeds (Cool-down, 5 minutes) Setup: None. Unit 2: Introducing Ratios, Lesson 9: Constant Speed 7

8 Student task statement Two trains are traveling at constant speeds on different tracks. Possible responses Train B is faster. Train A: Train B: Which train is traveling faster? Explain your reasoning. Unit 2: Introducing Ratios, Lesson 9: Constant Speed 8